Quantitative characterization of turbid media has been pursued intensely with a limited number of reflected light signals to determine optical parameters (1, 2). Achieving the same goal with reflectance image data, potentially consisting of 10,000 or more signals, remains a challenging problem despite its potentials for noninvasive detection and diagnosis (3). Optical characterization of turbid media can have wide-ranged applications to materials analysis in industry, lesion diagnosis in medicine and biological and chemical research but requires accurate models of light interaction with turbid media. For example, the radiative transfer theory is generally regarded as the most accurate optical model and uses three optical parameters to characterize a material: μa (absorption coefficient), μs (scattering coefficient) and g (anisotropy factor). However, the problems formulated on the basis of radiative transfer theory can be difficult to solve analytically without introducing various approximations.
One approximation of the radiative transfer theory is the diffusion model for photon transport. The diffusion model is an approximation of the radiative transfer theory in which all measured light is assumed to be scattered or “diffused.” The diffusion model is not as accurate as the radiative transfer model; however, the diffusion model can be used to determine μa and μs′ (reduced scattering coefficient=μs(1−g)). One potential advantage of using the diffusion model is that the results of the calculation are independent of the values of μs and g as long as μs′ remains the same. This can be referred to as the similarity principle. If the reflected light signals are dominated by the multiply scattered light, then the diffusion model may be relatively accurate. Therefore, the diffusion model and similarity principle can be applied with a sufficient degree of accuracy to the cases of large source-detector distances or materials with a relatively large ratio of μs to μa or to small values of g.
A noninvasive method of spatially resolved diffuse reflectance (SRDR) has been used extensively to determine μa and μs′ based on a diffusion model of reflectance signals measured with either continuous-wave (cw) or frequency modulated light (13-15). In this method a “point” source of scattered light is introduced into the sample at a small spot either through an optical fiber in contact with a sample or in the form of an incident beam focused at the sample surface. Reflected light signals are acquired at multiple locations of different source-detector distances (2, 16). The SRDR method could be implemented with an imager to replace the single detectors for non-contact acquisition of the reflectance signals through pixel binning (17-19). Further refinement of the image-based SRDR method was reported recently to separate μs and g from μs′, determined through a diffusion model, through the Monte Carlo simulations of a second reflectance image acquired with a focused beam of oblique incidence (20). Despite these improvements, however, the use of the diffusion model in the SRDR method often introduces errors in the inversely determined optical parameters if the signals are not dominated by multiply scattered light such as the cases of short source-detector distances and/or with samples of small a and/or large g. Furthermore, the SRDR method does not fully take the advantage of imaging, methods which favor full-field illumination since the pixel readings of an imager are of limited dynamic ranges in comparison to the single detectors. Finally, conventional methods of reflectance measurements, including the SRDR method, are generally not able to characterize heterogeneous turbid materials in which the optical parameters vary in different regions, such as in the case where one material is embedded in another material.
Optical fibers have been used in the SRDR methods to detect reflectance signals from a sample media. For example, U.S. Patent Publication No. 20060247532 to Ramanujam proposes an iterative process that determines the absorption and scattering coefficients of tissue from a set of diffuse reflectance measurements made with an optical spectrometer operating in the UV-VIS spectral range and using optical fibers to detect reflected light signals. The relationship between measured diffuse reflectance and the absorption and scattering coefficients is modeled using a Monte Carlo simulation based on a similarity principle to increase the speed of the simulation. However, this approach only determines μa, and μs′ rather than μa, μs and g.
In addition, the use of optical fibers in light detection can be prone to measurement errors because the fiber probes generally require direct contact with the sample medium. Furthermore, the optical fiber techniques discussed above may be limited to samples with homogeneous or homogeneously layered structures. Therefore, optical fiber detection of reflected light signals has limited usefulness especially in heterogeneous samples.